a$.$Briefly explains the training and classification algorithm for k$-$nearest neighbour learning.

$[4$ marks$]$

b$.$Determine the k$-$nearest neighbour prediction for the class of xq with F$1=2\mathrm{.}8$ and F$2=2\mathrm{.}8$ given dataset below with k$=1,$ k$=3$ and k$=5.$

F$1$ F$2$ Class

$1\mathrm{.}20\mathrm{.}8+$

$2\mathrm{.}32\mathrm{.}0-$

$2\mathrm{.}80\mathrm{.}8+$

$3\mathrm{.}72\mathrm{.}0-$

$2\mathrm{.}32\mathrm{.}8+$

$3\mathrm{.}73\mathrm{.}0-$

$2\mathrm{.}83\mathrm{.}0+$

$5\mathrm{.}23\mathrm{.}5-$

$1\mathrm{.}23\mathrm{.}5+$